First slide

Praticing questions using Newtons formule

Question

A block A of mass m and a pan P of equal mass are connected by a string passing over a smooth light pulley. Initially the system is at rest. A particle of mass m falls freely from height h on the pan and sticks to it. The speed with which A moves just after the collision is

Moderate

A

$\sqrt{\frac{g h}{2}}$
B

$\frac{\sqrt{2 g h}}{3}$
C

$\frac{2 \sqrt{g h}}{3}$
D

$\sqrt{\frac{2 g h}{3}}$

Solution

$v e l o c i t y w i t h w h i c h m a s s m h i t s t h e p a n i s \sqrt{2 g h} a t t h a t m o m e n t t o co n s e r v e t h e m o m e n t u m m \sqrt{2 g h} = 3 m v o t h e r m a s s i s a l s o c o n n e c t e d a n d m o v e s u p w i t h s a m e v e l o c i t y v = \frac{\sqrt{2 g h}}{3}$

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